TRIANGLES

FAROOQUI FIRDOUS JAHANPRESENTED BY

CONTENTS• TRIANGLES

1. DEFINITION2. TYPES3. PROPERTIES 4. SECONDARY PART 5. CONGRUENCY6. AREA

•TRIANGLESA triangle is a 3-sided polygon. Every triangle has three sides, three vertices and three angles.

•TYPES OF TRIANGLES

. On Basis of Length of Sides, there are 3 types of TrianglesEquilateral TriangleIsosceles TriangleScalene Triangle

On Basis of Angles, there are 3 types of triangles Acute Angled TriangleObtuse Angled TriangleRight Angled Triangle

EQUILATERAL TRIANGLETriangles having all sides equal are called Equilateral Triangle.

ISOSCELES TRIANGLETriangles having 2 sides equal are called Isosceles Triangle.

SCALENE TRIANGLETriangles having no sides equal are called Scalene Triangle.

Triangles whose all angles are acute angle are called Acute Angled Triangle.

ACUTE ANGLED TRIANGLE

RIGHT ANGLED TRIANGLE

OBTUSE ANGLED TRIANGLETriangles whose 1 angle is obtuse angle are called Obtuse Angled Triangle.

Triangles whose 1 angle is right angle are called Right Angled Triangle.

• PROPERTIES OF A TRIANGLEANGLE SUM PROPERTY

Angle sum Property of a Triangle is that the sum of all interior angles of a Triangle is equal to 180˚.

EXTERIOR ANGLE PROPERTY

Exterior angle Property of a Triangle is that An exterior angle of the Triangle is equal to sum of two opposite interior angles of the Triangle.

PYTHAGORAS THEOREM

Pythagoras Theorem is a theorem given by Pythagoras. The theorem is that In a Right Angled Triangle the square of the hypotenuse is equal to the sum of squares of the rest of the two sides.

HYPOTENUSE

• SECONDARY PART OF A TRIANGLEMEDIAN OF A TRIANGLE

The Line Segment joining the midpoint of the base of the Triangle is called Median of the Triangle.

OR

A Line Segment which connects a vertex of a Triangle to the midpoint of the opposite side is called Median of the Triangle.

MEDIAN

ALTITUDE OF A TRIANGLE

The Line Segment drawn from a Vertex of a Triangle perpendicular to its opposite side is called an Altitude or Height of a Triangle.

ALTITUDE

PERPENDICULAR BISECTOR

A line that passes through midpoint of the triangle or the line which bisects the third side of the triangle and is perpendicular to it is called the Perpendicular Bisector of that Triangle.

PERPENDICULAR BISECTOR

ANGLE BISECTOR

A line segment that bisects an angle of a triangle is called Angle Bisector of the triangle.

ANGLE BISECTOR

• CONGRUENCYSSS CRITERIA OF CONGRUENCY

If the three sides of one Triangle are equal to the three sides of another Triangle. Then the triangles are congruent by the SSS criteria.SSS criteria is called Side-Side-Side criteria of congruency.

SAS CRITERIA OF CONGRUENCY

If two sides and the angle included between them is equal to the corresponding two sides and the angle between them of another triangle. Then the both triangles are congruent by SAS criteria i.e. Side-Angle-Side Criteria of Congruency.

ASA CRITERIA OF CONGRUENCY

If two angles and a side of a Triangle is equal to the corresponding two angles and a side of the another triangle then the triangles are congruent by the ASA Criteria i.e. Angle-Side-Angle Criteria of Congruency.

RHS CRITERIA OF CONGRUENCY

If the hypotenuse, and a leg of one right angled triangle is equal to corresponding hypotenuse and the leg of another right angled triangle then the both triangles are congruent by the RHS criteria i.e. Right Angle-Hypotenuse-Side Criteria of Congruency.

• AREA OF TRAINGLEHERON’S FORMULA

Heron’s Formula can be used in finding area of all types of Triangles. The Formula is ::->

AREA = S = Semi-Perimeter a,b,c are sides of the Triangle

FORMULA FOR RIGHT ANGLED TRIANGLE

½ x base x height